How well does Transition
Mathematics address the content in the selected benchmarks?This
Transition Mathematics in Brief
The content ratings are estimates of what the textbook series attempts to present on only these benchmarks and are not an indication of overall content coverage or accuracy. The ratings also do not indicate whether or not the content will be learned. The instructional analysis provides information on the potential the series has for helping students actually learn the concepts and skills it attempts to present. The following indicates how well
All the benchmark ideas are addressed in this material, although each
idea is contained in only one or two lessons. In a lesson on multiplication of fractions,
the algebraic definition of division is provided as
All parts of this benchmark are addressed in many lessons and contexts throughout the book. Early lessons on converting fractions to decimals are extended to include writing mixed numbers as decimals. Later lessons present the procedure of simplifying fractions, which addresses the idea of equivalent fractions. The book presents equivalent ways of writing numbers, such as using powers of ten as exponents and in word form (thousand, billion) and writing expressions with exponents and bases. Significant coverage is devoted to the meaning of percent and the relation among percents, fractions, and decimals. Finally, algebraic approaches are used to convert decimals to fractions and to illustrate slopes as equivalent fractions.
Several chapters address the usual properties of triangles, rectangles, trapezoids, parallelograms, and circles. Special properties, such as the rigid structure of triangles and the area relationship to the boundary of a circle are not addressed specifically. The area of a triangle is developed from a rectangle, and polygons are divided into triangles to find their areas. A series of lessons looks at size changes by treating expansions and contractions of line segments, triangles, and polygons using coordinates. The ideas are extended and applied to maps and drawings.
All ideas of this benchmark are addressed in this material. Formulas are presented for the area of a square and rectangle, the volume of a cube, and the relation of volume to capacity. A more complete treatment is then given for the area model for multiplication, leading to the formula for the area of a rectangle, the area of a right triangle, and the calculation of other areas by decomposing figures into rectangles and triangles. The formulas for circumference and area of a circle are developed, practiced, and applied. Volumes of rectangular solids are developed, and the idea of measuring the size of two-dimensional objects is used to distinguish between calculating area and perimeter, which is then followed by the formula and calculation of areas of triangles, trapezoids, and parallelograms.
Several parts of this benchmark, such as the variable getting closer to some limiting value and reaching an intermediate minimum or maximum are never addressed. Most of the work on this benchmark is in two chapters; one that deals with data displays and another that presents coordinate graphs and equations. The latter chapter, which is the last chapter in the book, is more advanced and not intended for average students. Examples show decreases or increases over time, and students are asked to interpret the graphs. Several types of graphs illustrate the display of data, but only a few examples address directly the idea of steady or changing rate of increase or decrease. The last chapter briefly addresses the rate of increase, but there is little direct discussion of rates of change beyond noting the differing shapes of the graphs. One lesson deals with step graphs, addressing the part of the benchmark about increases or decreases in steps.
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